Problem 1: Non-differentiable utility with multiple constraints There are two goods, coffee and mineral water, available in arbitrary non- negative quantities (so the consumption set is R2). A consumer has pref- erences over consumption bundles that are represented by the following utility function: u(c, m) = min{c, m}+c+m, where c is the quantity of coffee (in grams) and m is the quantity of mineral water (in liters). The consumer has wealth in Dirhams of w> 0. The price of coffee is p > 0 (in grams/Dirham) and the price of mineral water q> 0 (in liters/Dirham). (a) In an appropriate diagram, illustrate the consumers map of indifference curves. Make sure you label the diagram clearly, and include as part of your answer any calculations about the slopes of the indifference curves. (b) Formulate and solve the consumer's utility maximization problem. Your final answer should describe the consumer's demand for coffee and mineral water as a function of the wealth w and the prices p and q, as well as the consumer's indirect utility function. Now assume that w = 100, p = 10 and q = 10. In addition to the monetary budget constraint, the consumer has a time constraint. The consumer has only 100 minutes available for the consumption of both goods. It takes 5 minutes/liter to consume water and and 20 minutes/gram to consume coffee. (e) In an appropriate diagram, illustrate the consumer's constraint set. Your diagram should illustrate the monetary budget constraint, the